What is 5x_{1}+7x_{2}=3,2x_{1}+4x_{2}=1 ?

The solution to 5x_{1}+7x_{2}=3,2x_{1}+4x_{2}=1 is x_{1}= 5/6 ,x_{2}=-1/6

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5x_{1}+7x_{2}=3,2x_{1}+4x_{2}=1

5 x_{1} + 7 x_{2} = 3, 2 x_{1} + 4 x_{2} = 1

x_{1} = \frac{5}{6}, x_{2} = - \frac{1}{6}

Solution steps

[5 x_{1} + 7 x_{2} = 3 2 x_{1} + 4 x_{2} = 1]

Isolate

x_{1}

for

5 x_{1} + 7 x_{2} = 3 : x_{1} = \frac{3 - 7 x _{2}}{5}

Substitute

x_{1} = \frac{3 - 7 x _{2}}{5}

[2 \cdot \frac{3 - 7 x _{2}}{5} + 4 x_{2} = 1]

Simplify

[\frac{6 + 6 x _{2}}{5} = 1]

Isolate

x_{2}

for

\frac{6 + 6 x _{2}}{5} = 1 : x_{2} = - \frac{1}{6}

For

x_{1} = \frac{3 - 7 x _{2}}{5}

Substitute

x_{2} = - \frac{1}{6}

x_{1} = \frac{3 - 7 ( - \frac{1}{6} )}{5}

\frac{3 - 7 ( - \frac{1}{6} )}{5} = \frac{5}{6}

x_{1} = \frac{5}{6}

The solutions to the system of equations are:

x_{1} = \frac{5}{6}, x_{2} = - \frac{1}{6}

2 y - x = - 9, 7 y - 2 x = 3

2 u + 3 v = 13, 4 u + 5 v = 23

3 x + 5 y = 38, 3 x - y = - 4

11 x + 5 y = 7, 6 x - 3 y = 21

6 x + 5 y = 4, 0.2 x + 0.3 y = 2

What is 5x_{1}+7x_{2}=3,2x_{1}+4x_{2}=1 ?
The solution to 5x_{1}+7x_{2}=3,2x_{1}+4x_{2}=1 is x_{1}= 5/6 ,x_{2}=-1/6